1 cup dried shiitake mushrooms (1.5 cups reconstituted)
2 carrots (approximately 2 cups) peeled and chopped roughly
1.5 cups leeks, chopped
3 kombu seaweed squares
3 cups water
1/4 cup sake
1/4 cup soy sauce
2 cups cooked noodles — I used soba
1 tablespoon oil
1.5 cups tofu
Cook soba noodles or any other kind of long, thin noodles according to package directions, set aside. You can use anything from tofu shirataki to ramen noodles to thin spaghetti or no noodles at all, it just depends on what you like.
Drain the tofu and cut it into thick slices. Blot the slices with a paper towel or a clean towel to absorb excess water. Cut the tofu into cubes. In a medium sized pan that can withstand high heat (I used a cast iron pan) heat one tablespoon oil until it smokes. Add tofu to the pan. Toss the tofu around until it browns on all sides, about two minutes. Take the tofu off heat and set it aside.
Soak the whole dried shiitakes in enough water to cover them (they will float) for 15 minutes in a bowl. Reserve the soaking water. In a medium sized pot, combine carrots, kombu squares, mushrooms and their soaking water, and three cups of water. Let it come to a boil and then reduce to medium. Allow it to simmer until carrots are slightly tender, about 7 minutes. Add leeks, soy sauce, and sake. Heat through, about one minute, then take off the heat.
Serve sukiyaki by ladling all the separate ingredients into bowls — carrots, leeks, mushrooms, tofu cubes, noodles — and then spooning broth over the whole thing.